This invention relates to electrical filters, and to methods of designing the same. More particularly, the invention relates to compensatory filters for hearing aids, and to the design of such filters.
From an examination of an aurally handicapped person, an audiologist can prepare an audiogram which is a plot of the threshold of aural acuity for pure tones in the most significant portion of the speech band of frequencies, say from 250-8000 Hz. Using the audiogram, the audiologist can prepare a frequency spectrum, unique to a patient, for specifying the compensatory amplification that a hearing aid must provide in order to overcome or at least minimize the patient's hearing deficiencies. Since deficiencies in aural acuity vary from patient to patient, and indeed, over time with the same patient, it is obvious that a wide variety of frequency spectrums exist for which hearing aids must provide compensation.
While there are many different types of hearing aids on the market, each with its own frequency spectrum characteristic, and while some minor alteration in frequency response can be achieved in a given hearing aid system to adapt it to a particular patient, the available frequency characteristics cannot possibly match the diverse characteristics required by aurally handicapped persons. Consequently, it is highly unlikely that a given hearing aid will provide perfect compensatory amplification for a given patient. In general, only partial compensation can be achieved, and the audiologist is forced to select a hearing aid which provides, in his judgement, the best compromise between what the patient requires and what the hearing aid will provide.
In order to provide improved compensatory amplification, it has been suggested to incorporate into a hearing aid, a compensatory filter whose frequency response characteristics will modify the frequency response of the instrument such that it provides amplification only at those frequencies at which acuity is deficient, and only in the amount deemed desirable for the patient being treated with the hearing aid. In order to be applicable to any patient regardless of where his particular hearing loss occurs, the filter must be capable of being designed to have a response over a band of frequencies closely matching an arbitrarily selected frequency spectrum. The parameters of the filter should also have the capability of being adjusted to modify the frequency characteristics of the filter in order to match changes in aural acuity of the user. In addition, such filter must be stable and must not introduce undesirable phase shift characteristics into the system, otherwise the hearing aid will not be able to amplify speech intelligibly notwithstanding the spectrum matching ability of the filter.
Discrete-time filters, known in the art as finite duration impulse response (FIR) filters or discrete impulse response (DIR) filters, can emphasize or suppress arbitrary frequencies within a given range of frequencies in a continuous waveform input. In theory, such filters would be ideally suited for on-line incorporation into a hearing aid, but in the form heretofore known, they have practical problems that militate against their use.
In its non-recursive form, an on-line discrete-time filter operates on a continuous waveform by multiplying present and past samples of the waveform by selected factors (i.e., the parameters of the filter), and arithmetically combines the result to produce, in real-time, a filtered waveform. In its recursive form, the filter performs a discrete convolution of previously computed values of the output waveform (i.e., the filtered waveform), and adds to this the discrete convolution of the input waveform (i.e., the original unfiltered waveform). The factors by which the past and present samples of the output waveform are multiplied are termed the auto-regressive parameters of the filter, and the factors by which the past and present samples of the original unfiltered waveform are multiplied are termed the moving-average parameters of the filter. As a consequence of this terminology, a filter of the type referred to above is termed an auto-regressive-moving-average (ARMA) type filter.
In general, the total number of the auto-regressive and moving-average parameters of an ARMA filter designed to match an arbitrarily selected frequency spectrum over a predetermined range of frequencies will be less than the number of parameters of a non-recursive filter designed for equal matching of the same frequency spectrum. See Reference [7], pgs. 216-218, and Reference [8].
One problem with incorporating conventional discrete-time filters into hearing aids is the size, weight and cost of these filters because of the number of parameters involved. Often, the number of parameters run into the hundreds as indicated in References [2] and [3]. A hardward implementation of such a filter requires the use of microprocessors and related microelectronic digital data-processing hardware, or microelectronic solid state tapped analog delay chips (TAD), depending upon whether the filter is entirely digital, entirely discrete-time-analog, or a hybrid combination of both. A non-recursive filter, or even a conventionally designed ARMA filter, whose number of parameters is not close to minimum, thus requires substantial hardware for implementation. This makes adjustment cumbersome. Furthermore, the filter becomes too expensive for a mass market such as that for hearing aids, and so heavy and bulky, when incorporated into a hearing aid, that the latter cannot be worn easily and comfortably.
Another problem with conventionally designed ARMA filters is the undesirable phase shift introduced by the filter, a factor of critical importance in a hearing aid where speech intelligibility depends on the phase as well as the amplitude characteristics of the frequency response of the filter. This problem has arisen because of concentration in the prior art on frequency domain optimization as indicated in Reference [4], with stability being achieved after optimization by shifting unstable poles of the filter to the stable region of the complex plane. Thus, there can be no guarantee that a conventionally designed ARMA filter, with an optimized amplitude-frequency spectrum characteristic, will have zero phase shift or a linear phase shift of arbitrary slope. In the absense of zero phase shift, or a linear relationship between phase and frequency, speech intelligibility can be reduced significantly even if compensatory amplitude/frequency spectrum fitting is achieved. Where phase proves to be a problem, the conventional approach is to increase (in fact, double) the number of parameters which increases the cost, weight and expense as indicated above.
Reference [5] suggests a time-domain design in which parameters are fitted directly to the impulse response function, but this approach cannot guarantee a stable, minimum parameter realization with a phase shift of zero or linear slope.
It is therefore an object of the present invention to provide a new and improved ARMA filter and a method for designing the same, wherein the filter overcomes or substantially avoids the deficiencies of the prior art as set forth above. Specifically, it is an object of the present invention to provide a minimum, or near minimum order, stable, ARMA filter whose amplitude frequency response closely matches an arbitrarily selected amplitude frequency spectrum, and whose phase response is zero or varies linearly with frequency at an arbitrarily selected slope.